Problem: Simplify the following expression: $\dfrac{12p^3}{60p^4}$ You can assume $p \neq 0$.
Answer: $ \dfrac{12p^3}{60p^4} = \dfrac{12}{60} \cdot \dfrac{p^3}{p^4} $ To simplify $\frac{12}{60}$ , find the greatest common factor (GCD) of $12$ and $60$ $12 = 2 \cdot 2 \cdot 3$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(12, 60) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{12}{60} \cdot \dfrac{p^3}{p^4} = \dfrac{12 \cdot 1}{12 \cdot 5} \cdot \dfrac{p^3}{p^4} $ $\phantom{ \dfrac{12}{60} \cdot \dfrac{3}{4}} = \dfrac{1}{5} \cdot \dfrac{p^3}{p^4} $ $ \dfrac{p^3}{p^4} = \dfrac{p \cdot p \cdot p}{p \cdot p \cdot p \cdot p} = \dfrac{1}{p} $ $ \dfrac{1}{5} \cdot \dfrac{1}{p} = \dfrac{1}{5p} $